Weak IDEA keys...

[jpp@markv.com]

  Well, I re-read the article, and here is the real dope.

In Crypto '93 Joan Daemen, Rene' Govaerts, and Joos Vandewalle write:

Abstract.  Large classes of weak keys have been found for the block
cipher algorithm IDEA, previously known as IPES [2].  IDEA has a
128-bit key and encrypts blocks of 64 bits.  For a class of 2^23 keys
IDEA exhibits a linear factor.  For certain class of 2^35 keys the
cipher has a global characteristic with probability 1.  For another
class of 2^51 keys only two encryptions and solving a set of 16
nonlinear boolean equations with 12 variables is sufficient to test if
the used key belongs to this class.  If it does, its particular value
can be calculated efficiently.  It is shown that the problem of weak
keys can be eliminated by slightly modifying the key schedual of IDEA.

[Typo's are probably mine :)]

  So, it isn't as bad as I thought.  Chances are about 2^51/2^128 ==
1/2^77 that you will get a bad key if you choose keys at random with
even distribution from the IDEA key space.  PGP tries to do exactly
this.  Once again, though, let me ask: has any one done anything about
implementing the _very_simple_ patch the authors describe?  PGP 2.5,
or 2.6 anyone?

  I am not _really_ paranoid, but I would hate it if a critical
message about the March 15th assassination plot were to fall into the
wrong hands because of a bad choice of IDEA keys.

  A related technical question: are there other easy to compute 2^n x
2^n -> 2^n 'invertable' functions than the three used in IDEA? (namely
(1) xor, (2) sum mod 2^n and (3) product mod (2^n)+1 with 0 taken to
represent 2^n.)

j'